%0 DATA
%A Alexandre, Zagoskin
%A Sergey, Saveliev
%A Franco, Nori
%D 2015
%T Modeling an adiabatic quantum computer via an exact map to a gas of particles
%U https://repository.lboro.ac.uk/articles/journal_contribution/Modeling_an_adiabatic_quantum_computer_via_an_exact_map_to_a_gas_of_particles/9409727
%2 https://repository.lboro.ac.uk/ndownloader/files/17027150
%K untagged
%X We map adiabatic quantum evolution on the classical Hamiltonian dynamics of a 1D gas (Pechukas gas) and simulate the latter numerically. This approach turns out to be both insightful and numerically efficient, as seen from our example of a CNOT gate simulation. For a general class of Hamiltonians we show that the escape probability from the initial state scales no faster than |\dot{\lambda}|^{\gamma}, where |\dot{\lambda}| is the adiabaticity parameter. The scaling exponent for the escape probability is \gamma = 1/2 for all levels, except the edge (bottom and top) ones, where \gamma <~1/3. In principle, our method can solve arbitrarily large adiabatic quantum Hamiltonians.